She walked close to Gatsby, touching his coat with her hand. . .
‘Did you see that?’ demanded Tom.
‘See what?’ He looked at me keenly, realizing that Jordan and I must have known all along.
‘You think I’m pretty dumb, don’t you?’ he suggested. ‘Perhaps I am, but I have a—almost a second sight, sometimes, that tells me what to do. Maybe you don’t believe that, but science—'
Tom is a fool. Every time I read this book, I get upset with Tom, because he thinks he is so smart and so entitled. Part of his feelings of entitlement have to do with money. Another part has to do with privilege. Tom feels that he is entitled to act any way he wants. That includes cheating on his wife.
First, the quote is ironic, because it shows that Tom is upset that Daisy is cheating on him even though he is doing the exact same thing.
Second, the quote is ironic because Tom is attempting to explain to Nick and Jordan just how smart he is. How smart is he? Well, according to Tom, he has a second sight or sixth sense. Basically, he believes that he has the intuitive power to accurately read all situations and perhaps even see into the future. It's ironic and ludicrous for Tom to say such foolery, because he is the last person to realize that anything is going on between Jay and Daisy. What is painfully obvious to everybody else is only just dawning on the guy who claims he has a "second sight."